{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:INFPADY24YHVFDGIXCOJOET65L","short_pith_number":"pith:INFPADY2","canonical_record":{"source":{"id":"1702.03691","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-13T09:50:50Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"1e1f311c8f7f105cd2a35b7fb6e0fb8c221a05a5adea7eec07d280b9715c4386","abstract_canon_sha256":"f7bf449523b02c5e6e9b8beda86054cced28eb0cf41742cfa97adbf6da4ecfbc"},"schema_version":"1.0"},"canonical_sha256":"434af00f1ae60f528cc8b89c97127eeacf9252eb69a6fb2c0b5d209f1e45578d","source":{"kind":"arxiv","id":"1702.03691","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03691","created_at":"2026-05-18T00:46:59Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03691v2","created_at":"2026-05-18T00:46:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03691","created_at":"2026-05-18T00:46:59Z"},{"alias_kind":"pith_short_12","alias_value":"INFPADY24YHV","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"INFPADY24YHVFDGI","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"INFPADY2","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:INFPADY24YHVFDGIXCOJOET65L","target":"record","payload":{"canonical_record":{"source":{"id":"1702.03691","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-13T09:50:50Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"1e1f311c8f7f105cd2a35b7fb6e0fb8c221a05a5adea7eec07d280b9715c4386","abstract_canon_sha256":"f7bf449523b02c5e6e9b8beda86054cced28eb0cf41742cfa97adbf6da4ecfbc"},"schema_version":"1.0"},"canonical_sha256":"434af00f1ae60f528cc8b89c97127eeacf9252eb69a6fb2c0b5d209f1e45578d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:59.069509Z","signature_b64":"qVsqiAloEctlH0c9fAuzvscUOGjI/+rVW6Oqa0+cAP55EX7U/rnKweb22ezN7RYrwoZ6DCpg661pPwrQXOZnDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"434af00f1ae60f528cc8b89c97127eeacf9252eb69a6fb2c0b5d209f1e45578d","last_reissued_at":"2026-05-18T00:46:59.069002Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:59.069002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.03691","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jnc57CWun67RuOCdQGGViz5A+6HxYSOe3DNteKK3c7OErEEhI1LY69PmMO/BYsKFNRaI9Xst7z4ID4760B2KBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:45:33.066488Z"},"content_sha256":"cdb35b204e5d1ba3c0da6ab2b548096f6cae39bb40cefce448fb170092c1bca2","schema_version":"1.0","event_id":"sha256:cdb35b204e5d1ba3c0da6ab2b548096f6cae39bb40cefce448fb170092c1bca2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:INFPADY24YHVFDGIXCOJOET65L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Siegel-Sternberg linearization theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"J\\\"urgen P\\\"oschel","submitted_at":"2017-02-13T09:50:50Z","abstract_excerpt":"We establish a general version of the Siegel-Sternberg linearization theorem for ultradiffentiable maps which includes the analytic case, the smooth case and the Gevrey case. It may regarded as a small divisior theorem without small divisor conditions. Along the way we give an exact characterization of those classes of ultradifferentiable maps which are closed under composition, and reprove regularity results for solutions of ode's and pde's. This will open up new directions in \\textsc{kam}-theory and other applications of ultradifferentiable functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03691","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YMsoKdUmEo6tRwf10fyICX5u4JrIVQltDttKryl/GqaiP7dSE8XweSmith93j4XiC5yaobcY4ZgliAVAnHdrCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:45:33.066833Z"},"content_sha256":"c622756b6b92553864c29b65b622bcd7f07b5e1c594f65e9146003ec11e64254","schema_version":"1.0","event_id":"sha256:c622756b6b92553864c29b65b622bcd7f07b5e1c594f65e9146003ec11e64254"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/INFPADY24YHVFDGIXCOJOET65L/bundle.json","state_url":"https://pith.science/pith/INFPADY24YHVFDGIXCOJOET65L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/INFPADY24YHVFDGIXCOJOET65L/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T21:45:33Z","links":{"resolver":"https://pith.science/pith/INFPADY24YHVFDGIXCOJOET65L","bundle":"https://pith.science/pith/INFPADY24YHVFDGIXCOJOET65L/bundle.json","state":"https://pith.science/pith/INFPADY24YHVFDGIXCOJOET65L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/INFPADY24YHVFDGIXCOJOET65L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:INFPADY24YHVFDGIXCOJOET65L","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f7bf449523b02c5e6e9b8beda86054cced28eb0cf41742cfa97adbf6da4ecfbc","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-13T09:50:50Z","title_canon_sha256":"1e1f311c8f7f105cd2a35b7fb6e0fb8c221a05a5adea7eec07d280b9715c4386"},"schema_version":"1.0","source":{"id":"1702.03691","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03691","created_at":"2026-05-18T00:46:59Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03691v2","created_at":"2026-05-18T00:46:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03691","created_at":"2026-05-18T00:46:59Z"},{"alias_kind":"pith_short_12","alias_value":"INFPADY24YHV","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"INFPADY24YHVFDGI","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"INFPADY2","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:c622756b6b92553864c29b65b622bcd7f07b5e1c594f65e9146003ec11e64254","target":"graph","created_at":"2026-05-18T00:46:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We establish a general version of the Siegel-Sternberg linearization theorem for ultradiffentiable maps which includes the analytic case, the smooth case and the Gevrey case. It may regarded as a small divisior theorem without small divisor conditions. Along the way we give an exact characterization of those classes of ultradifferentiable maps which are closed under composition, and reprove regularity results for solutions of ode's and pde's. This will open up new directions in \\textsc{kam}-theory and other applications of ultradifferentiable functions.","authors_text":"J\\\"urgen P\\\"oschel","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-13T09:50:50Z","title":"On the Siegel-Sternberg linearization theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03691","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cdb35b204e5d1ba3c0da6ab2b548096f6cae39bb40cefce448fb170092c1bca2","target":"record","created_at":"2026-05-18T00:46:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f7bf449523b02c5e6e9b8beda86054cced28eb0cf41742cfa97adbf6da4ecfbc","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-13T09:50:50Z","title_canon_sha256":"1e1f311c8f7f105cd2a35b7fb6e0fb8c221a05a5adea7eec07d280b9715c4386"},"schema_version":"1.0","source":{"id":"1702.03691","kind":"arxiv","version":2}},"canonical_sha256":"434af00f1ae60f528cc8b89c97127eeacf9252eb69a6fb2c0b5d209f1e45578d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"434af00f1ae60f528cc8b89c97127eeacf9252eb69a6fb2c0b5d209f1e45578d","first_computed_at":"2026-05-18T00:46:59.069002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:59.069002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qVsqiAloEctlH0c9fAuzvscUOGjI/+rVW6Oqa0+cAP55EX7U/rnKweb22ezN7RYrwoZ6DCpg661pPwrQXOZnDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:59.069509Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.03691","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdb35b204e5d1ba3c0da6ab2b548096f6cae39bb40cefce448fb170092c1bca2","sha256:c622756b6b92553864c29b65b622bcd7f07b5e1c594f65e9146003ec11e64254"],"state_sha256":"815477bb602e78f3dd8457c16e674718273ba072726b95eb8b15958882da89c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CNm1LJuMifKhyHSoN9qmVv4Op0zAO6M3tyo+MIQoEMBIrTr+3zzaAx0/pZE3vAEE0mM8pDykNZT6zYi9Z5deCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T21:45:33.068773Z","bundle_sha256":"3d67406b5ae6de8d9823a2a7fefbde17ef2432c5a51cca35d40e1974bd3cd96d"}}